Overtreffende telling van elk element in de array
Gegeven een array van verschillende gehele getallen arr[] a overtreffen van een element arr[i] is elk element arr[j] zodat j > i en arr[j] > arr[i]. Zoek het aantal overtreders voor elk element in de array.
Voorbeelden:
Invoer: arr[] = [2 7 5 3 8 1]
Uitgang: [4 1 1 1 0 0]
Uitleg: Voor 2 zijn er rechts 4 grotere elementen: [7 5 3 8]
Voor 7 is er rechts daarvan 1 groter element: [8]
Voor 5 is er 1 groter element rechts ervan: [8]
Voor 3 is er 1 groter element rechts ervan: [8]
Voor 8 is er rechts geen groter element: [0]
Voor 1 is er rechts geen groter element: [0]Invoer: arr[] = [4 5 1]
Uitgang: [1 0 0]
Uitleg: Voor 4 is er rechts daarvan 1 groter element: [5]
Voor 5 is er rechts geen groter element: [0]
Voor 1 is er rechts geen groter element: [0]
Inhoudsopgave
- [Naïeve aanpak] - Twee geneste lussen gebruiken - O(n^2) Tijd en O(1) Ruimte
- [Verwachte aanpak] - Samenvoegstap van samenvoegsortering gebruiken - O(n Log n) Tijd en O(n) Ruimte
[Naïeve aanpak] - Twee geneste lussen gebruiken - O(n^2) Tijd en O(1) Ruimte
De eenvoudigste aanpak is om herhalen door de array en voor elk element graaf het aantal elementen ervan rechts dat is groter dan het.
C++ #include #include using namespace std ; vector < int > findSurpasser ( vector < int > & arr ) { int n = arr . size (); // array to store surpasser counts vector < int > res ( n 0 ); for ( int i = 0 ; i < n ; i ++ ) { // Find surpasser for arr[i] int count = 0 ; for ( int j = i + 1 ; j < n ; j ++ ) { if ( arr [ j ] > arr [ i ]) count ++ ; } res [ i ] = count ; } return res ; } int main () { vector < int > arr = { 2 7 5 3 8 1 }; vector < int > res = findSurpasser ( arr ); for ( int count : res ) cout < < count < < ' ' ; return 0 ; }
C #include #include int * findSurpasser ( int arr [] int n ) { // Array to store surpasser counts int * res = ( int * ) malloc ( n * sizeof ( int )); for ( int i = 0 ; i < n ; i ++ ) { // Find surpasser for arr[i] int count = 0 ; for ( int j = i + 1 ; j < n ; j ++ ) { if ( arr [ j ] > arr [ i ]) count ++ ; } res [ i ] = count ; } return res ; } int main () { int arr [] = { 2 7 5 3 8 1 }; int n = sizeof ( arr ) / sizeof ( arr [ 0 ]); int * res = findSurpasser ( arr n ); for ( int i = 0 ; i < n ; i ++ ) printf ( '%d ' res [ i ]); return 0 ; }
Java import java.util.ArrayList ; class GfG { static ArrayList < Integer > findSurpasser ( int [] arr ) { int n = arr . length ; // List to store surpasser counts ArrayList < Integer > res = new ArrayList <> (); for ( int i = 0 ; i < n ; i ++ ) { // Find surpasser for arr[i] int count = 0 ; for ( int j = i + 1 ; j < n ; j ++ ) { if ( arr [ j ] > arr [ i ] ) count ++ ; } res . add ( count ); } return res ; } public static void main ( String [] args ) { int [] arr = { 2 7 5 3 8 1 }; ArrayList < Integer > res = findSurpasser ( arr ); for ( int count : res ) System . out . print ( count + ' ' ); } }
Python def findSurpasser ( arr ): n = len ( arr ) # List to store surpasser counts res = [ 0 ] * n for i in range ( n ): # Find surpasser for arr[i] count = 0 for j in range ( i + 1 n ): if arr [ j ] > arr [ i ]: count += 1 res [ i ] = count return res if __name__ == '__main__' : arr = [ 2 7 5 3 8 1 ] result = findSurpasser ( arr ) for val in result : print ( val end = ' ' )
C# using System ; using System.Collections.Generic ; class GfG { static List < int > findSurpasser ( int [] arr ) { int n = arr . Length ; // List to store surpasser counts List < int > res = new List < int > (); for ( int i = 0 ; i < n ; i ++ ) { // Find surpasser for arr[i] int count = 0 ; for ( int j = i + 1 ; j < n ; j ++ ) { if ( arr [ j ] > arr [ i ]) count ++ ; } res . Add ( count ); } return res ; } static void Main ( string [] args ) { int [] arr = { 2 7 5 3 8 1 }; List < int > result = findSurpasser ( arr ); foreach ( int count in result ) Console . Write ( count + ' ' ); } }
JavaScript function findSurpasser ( arr ) { const n = arr . length ; // array to store surpasser counts let res = new Array ( n ). fill ( 0 ); for ( let i = 0 ; i < n ; i ++ ) { // Find surpasser for arr[i] let count = 0 ; for ( let j = i + 1 ; j < n ; j ++ ) { if ( arr [ j ] > arr [ i ]) count ++ ; } res [ i ] = count ; } return res ; } // Driver Code const arr = [ 2 7 5 3 8 1 ]; const result = findSurpasser ( arr ); console . log ( result . join ( ' ' ));
Uitvoer
4 1 1 1 0 0
[Verwachte aanpak] - Samenvoegstap van samenvoegsortering gebruiken - O(n Log n) Tijd en O(n) Ruimte
Bij deze aanpak gebruiken we de stap samenvoegen van Wandelingen . Als tijdens de fusie de it element in de linkerhelft is kleiner dan de jde element in de rechterhelft betekent het dat alles overig elementen in de rechterhelft (van j tot eind) Zijn groter dan de it element in de linkerhelft (aangezien beide helften gesorteerd ). Daarom voegen we het aantal toe overige elementen in de rechterhelft van de tel overtreffen van de it onderdeel van de linkerhelft. Dit proces wordt herhaald voor alle elementen in de linkerhelft wanneer ze worden samengevoegd met de rechterhelft.
Omdat alle elementen in de array dat zijn verschillend wij gebruiken een hash-kaart om het aantal overtreders voor elk element op te slaan. Nadat het samenvoegen is voltooid, vullen we de resultaatarray met de overtreffende tellingen, waarbij dezelfde volgorde wordt aangehouden als de oorspronkelijke invoer.
C++ #include #include #include using namespace std ; // Merge function to sort the array and update surpasser counts int merge ( vector < int > & arr int lo int mid int hi unordered_map < int int > & m ) { int n1 = mid - lo + 1 ; int n2 = hi - mid ; vector < int > left ( n1 ) right ( n2 ); // Copy data into temporary arrays left[] and right[] for ( int i = 0 ; i < n1 ; i ++ ) left [ i ] = arr [ lo + i ]; for ( int j = 0 ; j < n2 ; j ++ ) right [ j ] = arr [ mid + 1 + j ]; int i = 0 j = 0 k = lo ; // Merging two halves while ( i < n1 && j < n2 ) { // All elements in right[j..n2] are greater than left[i] // So add n2 - j in surpasser count of left[i] if ( left [ i ] < right [ j ]) { m [ left [ i ]] += n2 - j ; arr [ k ++ ] = left [ i ++ ]; } else { arr [ k ++ ] = right [ j ++ ]; } } // Copy remaining elements of left[] if any while ( i < n1 ) arr [ k ++ ] = left [ i ++ ]; // Copy remaining elements of right[] if any while ( j < n2 ) arr [ k ++ ] = right [ j ++ ]; } void mergeSort ( vector < int > & arr int lo int hi unordered_map < int int > & m ) { if ( lo < hi ) { int mid = lo + ( hi - lo ) / 2 ; // Sort left and right half mergeSort ( arr lo mid m ); mergeSort ( arr mid + 1 hi m ); // Merge them merge ( arr lo mid hi m ); } } vector < int > findSurpasser ( vector < int >& arr ) { int n = arr . size (); // Map to store surpasser counts unordered_map < int int > m ; // Duplicate array to perform merge Sort // so that orginial array is not modified vector < int > dup = arr ; mergeSort ( dup 0 n - 1 m ); // Store surpasser counts in result array // in the same order as given array vector < int > res ( n ); for ( int i = 0 ; i < n ; i ++ ) res [ i ] = m [ arr [ i ]]; return res ; } int main () { vector < int > arr = { 2 7 5 3 8 1 }; vector < int > res = findSurpasser ( arr ); for ( int count : res ) cout < < count < < ' ' ; return 0 ; }
Java import java.util.List ; import java.util.Map ; import java.util.HashMap ; import java.util.ArrayList ; class GfG { // Merge function to sort the array // and update surpasser counts static void merge ( int [] arr int lo int mid int hi Map < Integer Integer > m ) { int n1 = mid - lo + 1 ; int n2 = hi - mid ; int [] left = new int [ n1 ] ; int [] right = new int [ n2 ] ; // Copy data into temporary arrays left[] and right[] for ( int i = 0 ; i < n1 ; i ++ ) left [ i ] = arr [ lo + i ] ; for ( int j = 0 ; j < n2 ; j ++ ) right [ j ] = arr [ mid + 1 + j ] ; int i = 0 j = 0 k = lo ; // Merging two halves while ( i < n1 && j < n2 ) { // All elements in right[j..n2] are greater than left[i] // So add n2 - j to surpasser count of left[i] if ( left [ i ] < right [ j ] ) { m . put ( left [ i ] m . getOrDefault ( left [ i ] 0 ) + n2 - j ); arr [ k ++] = left [ i ++] ; } else { arr [ k ++] = right [ j ++] ; } } // Copy remaining elements of left[] if any while ( i < n1 ) arr [ k ++] = left [ i ++] ; // Copy remaining elements of right[] if any while ( j < n2 ) arr [ k ++] = right [ j ++] ; } static void mergeSort ( int [] arr int lo int hi Map < Integer Integer > m ) { if ( lo < hi ) { int mid = lo + ( hi - lo ) / 2 ; // Sort left and right halves mergeSort ( arr lo mid m ); mergeSort ( arr mid + 1 hi m ); // Merge them merge ( arr lo mid hi m ); } } static ArrayList < Integer > findSurpasser ( int [] arr ) { int n = arr . length ; // Map to store surpasser counts Map < Integer Integer > m = new HashMap <> (); // Duplicate array to perform merge sort int [] dup = arr . clone (); mergeSort ( dup 0 n - 1 m ); // Store surpasser counts in result list ArrayList < Integer > res = new ArrayList <> (); for ( int i = 0 ; i < n ; i ++ ) res . add ( m . getOrDefault ( arr [ i ] 0 )); return res ; } public static void main ( String [] args ) { int [] arr = { 2 7 5 3 8 1 }; ArrayList < Integer > res = findSurpasser ( arr ); for ( int count : res ) System . out . print ( count + ' ' ); } }
Python def merge ( arr lo mid hi m ): n1 = mid - lo + 1 n2 = hi - mid left = arr [ lo : lo + n1 ] right = arr [ mid + 1 : mid + 1 + n2 ] i = j = 0 k = lo # Merging two halves while i < n1 and j < n2 : # All elements in right[j..n2] are greater than left[i] # So add n2 - j in surpasser count of left[i] if left [ i ] < right [ j ]: m [ left [ i ]] += n2 - j arr [ k ] = left [ i ] i += 1 else : arr [ k ] = right [ j ] j += 1 k += 1 # Copy remaining elements of left[] if any while i < n1 : arr [ k ] = left [ i ] i += 1 k += 1 # Copy remaining elements of right[] if any while j < n2 : arr [ k ] = right [ j ] j += 1 k += 1 def mergeSort ( arr lo hi m ): if lo < hi : mid = lo + ( hi - lo ) // 2 # Sort left and right half mergeSort ( arr lo mid m ) mergeSort ( arr mid + 1 hi m ) # Merge them merge ( arr lo mid hi m ) def findSurpasser ( arr ): n = len ( arr ) # Map to store surpasser counts m = { key : 0 for key in arr } # Duplicate array to perform merge Sort # so that original array is not modified dup = arr [:] mergeSort ( dup 0 n - 1 m ) # Store surpasser counts in result array # in the same order as given array res = [ m [ arr [ i ]] for i in range ( n )] return res if __name__ == '__main__' : arr = [ 2 7 5 3 8 1 ] result = findSurpasser ( arr ) for val in result : print ( val end = ' ' )
C# using System ; using System.Collections.Generic ; class GfG { // Merge function to sort the array // and update surpasser counts static void merge ( int [] arr int lo int mid int hi Dictionary < int int > m ) { int n1 = mid - lo + 1 ; int n2 = hi - mid ; int [] left = new int [ n1 ]; int [] right = new int [ n2 ]; // Copy data into temporary arrays for ( int i = 0 ; i < n1 ; i ++ ) left [ i ] = arr [ lo + i ]; for ( int j = 0 ; j < n2 ; j ++ ) right [ j ] = arr [ mid + 1 + j ]; int i1 = 0 j1 = 0 k = lo ; // Merge the two halves while ( i1 < n1 && j1 < n2 ) { // Count surpassers if ( left [ i1 ] < right [ j1 ]) { if ( ! m . ContainsKey ( left [ i1 ])) m [ left [ i1 ]] = 0 ; m [ left [ i1 ]] += n2 - j1 ; arr [ k ++ ] = left [ i1 ++ ]; } else { arr [ k ++ ] = right [ j1 ++ ]; } } // Copy remaining elements while ( i1 < n1 ) arr [ k ++ ] = left [ i1 ++ ]; while ( j1 < n2 ) arr [ k ++ ] = right [ j1 ++ ]; } static void mergeSort ( int [] arr int lo int hi Dictionary < int int > m ) { if ( lo < hi ) { int mid = lo + ( hi - lo ) / 2 ; // Recursive sort mergeSort ( arr lo mid m ); mergeSort ( arr mid + 1 hi m ); // Merge sorted halves merge ( arr lo mid hi m ); } } static List < int > findSurpasser ( int [] arr ) { int n = arr . Length ; Dictionary < int int > m = new Dictionary < int int > (); int [] dup = new int [ n ]; Array . Copy ( arr dup n ); mergeSort ( dup 0 n - 1 m ); List < int > res = new List < int > (); for ( int i = 0 ; i < n ; i ++ ) { res . Add ( m . ContainsKey ( arr [ i ]) ? m [ arr [ i ]] : 0 ); } return res ; } static void Main () { int [] arr = { 2 7 5 3 8 1 }; List < int > res = findSurpasser ( arr ); foreach ( int count in res ) Console . Write ( count + ' ' ); } }
JavaScript function merge ( arr lo mid hi m ) { const n1 = mid - lo + 1 ; const n2 = hi - mid ; const left = []; const right = []; // Copy data into temporary arrays left[] and right[] for ( let i = 0 ; i < n1 ; i ++ ) left [ i ] = arr [ lo + i ]; for ( let j = 0 ; j < n2 ; j ++ ) right [ j ] = arr [ mid + 1 + j ]; let i = 0 j = 0 k = lo ; // Merging two halves while ( i < n1 && j < n2 ) { // All elements in right[j..n2] are greater than left[i] // So add n2 - j in surpasser count of left[i] if ( left [ i ] < right [ j ]) { m [ left [ i ]] = ( m [ left [ i ]] || 0 ) + n2 - j ; arr [ k ++ ] = left [ i ++ ]; } else { arr [ k ++ ] = right [ j ++ ]; } } // Copy remaining elements of left[] if any while ( i < n1 ) arr [ k ++ ] = left [ i ++ ]; // Copy remaining elements of right[] if any while ( j < n2 ) arr [ k ++ ] = right [ j ++ ]; } function mergeSort ( arr lo hi m ) { if ( lo < hi ) { const mid = Math . floor ( lo + ( hi - lo ) / 2 ); // Sort left and right half mergeSort ( arr lo mid m ); mergeSort ( arr mid + 1 hi m ); // Merge them merge ( arr lo mid hi m ); } } function findSurpasser ( arr ) { const n = arr . length ; // Map to store surpasser counts const m = {}; // Duplicate array to perform merge Sort // so that original array is not modified const dup = arr . slice (); mergeSort ( dup 0 n - 1 m ); // Store surpasser counts in result array // in the same order as given array const res = []; for ( let i = 0 ; i < n ; i ++ ) res . push ( m [ arr [ i ]] || 0 ); return res ; } // Driver Code const arr = [ 2 7 5 3 8 1 ]; const res = findSurpasser ( arr ); console . log ( res . join ( ' ' ));
Uitvoer
4 1 1 1 0 0
Gerelateerde artikelen:
- Inversietelling
- Wandelingen
